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      On the reality of the quantum state

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          Abstract

          Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds directly to reality. However, there is a long history of suggestions that a quantum state (even a pure state) represents only knowledge or information about some aspect of reality. Here we show that any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions which contradict those of quantum theory.

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          The Statistical Interpretation of Quantum Mechanics

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            Contextuality for preparations, transformations, and unsharp measurements

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              Quantum probabilities as Bayesian probabilities

              , , (2001)
              In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental law, probabilities for individual quantum systems can be understood within the Bayesian approach. We argue that the distinction between classical and quantum probabilities lies not in their definition, but in the nature of the information they encode. In the classical world, maximal information about a physical system is complete in the sense of providing definite answers for all possible questions that can be asked of the system. In the quantum world, maximal information is not complete and cannot be completed. Using this distinction, we show that any Bayesian probability assignment in quantum mechanics must have the form of the quantum probability rule, that maximal information about a quantum system leads to a unique quantum-state assignment, and that quantum theory provides a stronger connection between probability and measured frequency than can be justified classically. Finally we give a Bayesian formulation of quantum-state tomography.
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                Author and article information

                Journal
                14 November 2011
                2012-11-18
                Article
                10.1038/nphys2309
                1111.3328
                3bf32a3d-15e0-4146-962c-9b81960fb69e

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Nature Phys. 8, 475 (2012)
                5+3 pages, 3+2 figures. v3: Minor improvements, now closely approximates journal version
                quant-ph

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